Specific Heat Capacity

Specific Heat Capacity
INTRODUCITON
Heat (symbolized by Q) is a form of kinetic energy produced by the motion of atoms and
molecules and is transferred from one body or system to another due to a difference in
temperature. This energy is transferred from a hotter object to a cooler object. In order for energy
to be conserved, the amount of heat energy lost by the hotter object plus amount of heat energy
gained by the cooler object must be equal to zero.
ΔQ H + ΔQ C = 0 (Eq. 1)
The subscripts H and C indicate the hot and cold object. The amount of heat energy an object can
absorb or release (ΔQ) is directly related to the following factors: how much mass the object has,
how easy/hard it is for the material to absorb/release heat energy (otherwise known as the
specific heat = c), and how much the object’s temperature changes (ΔT).
ΔQ = mcΔT = mc (T f – T i ) (Eq. 2)
When two objects come to a thermal equilibrium, that means that they have the same final
temperature. The cool object gains the heat energy that the cool object loses. Therefore, the
conservation of energy equation may be rewritten as follows:
[m H c H (T f – T H )] + [m C c C (T f – T C )] = 0 (Eq. 3)
The specific heat capacity (c) indicates amount of energy (in Joules) required to raise the
temperature of 1 kg of a particular material by 1 degree Celsius. Its units are J/(kgºC). The
specific heat is a property of the material and every substance has a different specific heat. It
takes a different amount of energy to raise the temperature of 1 kg of each material by 1 ºC.
More energy is required to increase the temperature of a substance with high specific heat than
one with low specific heat. For example, the specific heat of water is 4186 J/(kgºC). This means
that it takes 4186 Joules to raise the temperature of 1 kg of water by 1 ºC. In fact, water is one of
the more difficult materials to change the temperature of. A short list of specific heat values is
included in Table 1.

Table 1. Specific heat of common materials
Reminder: Record in your lab report ALL measured values. Be sure to include what instrument
you measured it with, the units, and the estimated error, and the instrument the measurement was
made with. When performing a calculation be sure to always write the equation used first, then
insert the values AND THEIR UNITS, then show your work in solving the equation including
any unit conversions.
PRELAB QUESTIONS
Aluminum Water Copper Tin Iron
c [J/kgºC] 900 4186 386 227 450
1. If you have 1.0 g of water and 1.0 g of aluminum both at 20.0 ºC, which would need to
receive more energy to increase its temperature to 21.0 ºC Explain.
2. If you have 1.0 g of water and 5.0 g of aluminum both at 20.0 ºC, which would need to
absorb more energy to increase its temperature to 21.0 ºC Explain.
3. If you mixed 0.200 kg of water at 30.0 ºC with 0.400 kg of water at 50.0 ºC, what would
be the temperature of the mixture
4. You have .070 kg of an unknown sample that is at 96.0 ºC. You drop it into 0.150 kg of
water that is at 20.0 ºC. After a few seconds, the temperature of the water stabilizes at
23.6 ºC. Which of the materials in Table 1 is the unknown sample most likely to be
MATERIALS
Styrofoam container
Two cups
Metal Samples
Thermometer
Mass balance
ACTIVITY I: Determining the final temperature of a water mixture.
5. In this activity you will use Eq. 3 to predict the final temperature of a mixture of hot
and cold water. Start with around half a cup of cool water from the water fountain
around half a cup of hot water from the sink. (Let the hot water run until it is really
hot!) Do not mix the water yet. First determine what quantities must be known in
order to make an informed prediction of the final temperature. If you need to make

any measurements, remember to also record the units, the uncertainty, and the
measuring device that you used. Also remember to calibrate and zero any measuring
device before using it.
6. Given what you have measured, rearrange Eq. 3 to predict the final temperature of the
water mixture. Show your work!
7. Pour the contents of the beaker into the Styrofoam container and stir with the
thermometer. Record the highest temperature reached by the mixture. Using percent
difference, compare your measured value to your predicted value. Explain any
differences in your error analysis.
ACTIVITY II: Determining the specific heat of a metal sample.
QUESTIONS
8. In this activity you will use Eq. 3 to determine the specific heat of a metal cylinder.
You will heat the cylinder in a beaker of hot water from the sink, then quickly
transfer the cylinder to a Styrofoam container of cool water, stirring with the
thermometer until the water and the sample have reached a final equilibrium
temperature. The Styrofoam container must contain enough water to completely
cover the metal cylinder. As in Activity I, determine, measure, and record the
quantities that must be known in order to make a determination of the specific heat of
the sample.
9. Given what you have measured, rearrange Eq. 3 to determine the specific heat of the
metal. Show your work!
10. According to Table 1, what type of metal is the sample most likely made of Do you
agree Compare the specific heat you calculated to the value in the table using
percent difference.
11. Was all of the heat energy of the metal sample actually transferred to the water
Explain.
12. Where could the heat have gone If energy was somehow lost, would this cause your
determination of specific heat to be higher or lower than the predicted value Explain.